Brady's father, Tom Brady Sr., told The Boston Globe on Friday that reports of his son's engagement were "rumor, rumor, rumor ... We don't know a thing about it. Nobody told me. We talked to him and there's nothing to say."

The Boston Herald reported that the couple strolled down Bean Town's Beacon Street on Friday – and that Bündchen, 28, was without an engagement ring.

Bündchen's twin sister, Patricia, also denied the report, saying in an e-mail that the engagement story – which first surfaced on TMZ – is "not true."

Reached by PEOPLE, Bündchen's rep declined to comment. Stacey James, a spokesman for the Patriots, responded, "I heard the report that he [proposed] on a plane, but I don't think it's true." Still, he added, "Tom keeps his private life private."